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A146212
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Number of intersection points of all lines through the vertices of a regular n-gon.
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15
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3, 5, 15, 37, 91, 145, 333, 471, 891, 901, 1963, 2185, 3795, 3969, 6681, 5563, 10963, 11141, 17031, 17293, 25323, 21913, 36325, 36479, 50571, 50485, 68643, 51661, 91171, 90753, 118833, 118355, 152355, 139861, 192511, 191445, 240123, 238481
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history;
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OFFSET
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3,1
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COMMENTS
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This includes intersection points outside of the n-gon. Note that for odd n, n divides a(n); for even n, n divides a(n)-1. For odd n, it appears that a(n)=n(n^3-7n^2+15n-1)/8.
That formula is correct: see the Sidorenko link. - N. J. A. Sloane, Sep 12 2021
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LINKS
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Scott R. Shannon, Image for n = 3. In this and other images the dots showing the regular n-gon's vertices are slightly larger and circled with white for clarity. The dot color key is at the top-left of the image.
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FORMULA
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There is a formula for odd n: see Comment section and the Sidorenko link. - N. J. A. Sloane, Sep 12 2021
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EXAMPLE
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a(5)=15 because there are 5 points inside the pentagon, 5 points on the pentagon and five points outside of the pentagon.
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CROSSREFS
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KEYWORD
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nice,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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